html, body {
    font-size: 16px;
    height: 100%;
    font-family: Arial, Helvetica, sans-serif;
    color: #3C4142;
}


.navbar-fixed-top-black{
    margin: 0px auto;
    padding: 0px;
    display:block;
    width: 72%;
    height: 56px;
    overflow: hidden;
    justify-content: center; 
    text-align: center;
    position: relative;
    top: 0;
    font-family: 'Archivo Narrow';
    border-bottom: 1px solid black;
}

.navbar-fixed-top-black ul {
    justify-content: center;    
    margin-left: auto;
    margin-right: auto;
    
}
.navbar-fixed-top-black li{
    padding: 0px 72px;
    /* this puts all options in a singular row*/
    display: inline;
}

.navbar-fixed-top-black a {
    color:black;
    text-decoration: none; 
}

.navbar-fixed-top-black a:hover {
    text-decoration: underline;
}

/* sizing for all content below nav */
.content{
    width: 70%;
    margin: 0px auto;
}

h1 {
    margin: auto 0;
    font-family: 'Bebas Neue';
    font-size: 3rem;
    text-align: center;
    padding-top: 60px;
    padding-bottom: 60px;
}

/* about 40px between h1 and h2, not sure why, might need to put them in a sole container */
h2 {
    font-family: 'Bebas Neue';
    font-size: 1.5rem;
    color: #0B5394;
   
}

h3 /*main section headings 1,2,etc*/ {
    font-size: 1.15rem;
    margin-top: 42px;
    color: #3d85c6;
}

/*spacing between sections & paragrphs */

#questionone /* first line under title heading */ {
    padding-top: 0px;
}

.sect /*main section headings 1,2,etc*/ {
    font-size: 1.15rem;
    margin-top: 42px;
    color: #3d85c6;
}

.sect1 /*section heading directly following main section heading #.x */{
    font-size: 1rem;
    color: #3d85c6;
    margin-bottom: -5px;
}

.sect1b /*section heading directly following main section heading #.x.y */{
    font-size: 1rem;
    color: #3d85c6;
    margin-top: 20px;
    margin-bottom: -5px;
    font-style: italic;
    font-weight: 200px;
   
}

.sect2{
    font-size: 1rem;
    color: #3d85c6;
    margin-top: 36px;
    margin-bottom: -5px;
    font-style: italic;
    font-weight: 200px;
}

.sect2b{
    font-size: 1rem;
    color: #3d85c6;
    margin-top: 20px;
    margin-bottom: -5px;
    font-style: italic;
    font-weight: 200px;
}



#questionone {
    padding-top: 0px;
}

h4 {
    text-decoration: underline;
}
/*  underlining task headers within equations section*/
.unders {
    text-decoration: underline;
}

#probsoltwo{
    padding-top: 45px;
}

.code_used {
    background-color: #e6f3d8;
    color: green;
    padding-top: 10px;
    padding-bottom: 10px;
    width: 100%;
    text-align: center;
}



img {
    margin: 0 auto;
    display: block;
    border: 1px solid gray;
    width: 100%;
    
}

.image{
    width: 40%;
    height: auto;
    margin: 0 auto;
    display: block;
}

.image2{
    width: 80%;
    height: auto;
    margin: 0 auto;
    display: block;
}

.image3{
    width: 60%;
    height: auto;
    margin: 0 auto;
    display: block;
}

.graphcap {
    font-size: .9rem;
    text-align: center;
}


/*for equations */

.function {
    font-weight: bold;
}

.eq {
    line-height: 2;
    text-indent: 100px;
}

.eq1 {
    text-indent: 180px;
}

.eq2 {
    text-indent: 200px;
}

#rightside {
    float: right;
}


/*spacing betweeen graphs, images & text paragraphs*/


.underimage {
    padding-top: 30px;
}

.abovegraph {
    margin-bottom: 75px;
}

.abovegraph1{
    margin-bottom: 45px;
}

.shorterdist {
    margin-bottom: -10px;
}

.equation{
    overflow: scroll;
}

/* 'let' variable section- indenting and spacing all equations */



/* bold and line spacingwithin paragraphs*/
.bold {
    font-weight: bold;
}

.ital {
    font-style: italic;
    font-family: "Lora";
}

.text {
    line-height: 1.75;
}

#variables p {
    margin-bottom: -20px;
    text-indent: 100px;
}


.indent {
    text-indent: 200px;
}

.indent1 {
    text-indent: 250px;
    margin-bottom: 30px;
}

.indent2 {
    text-indent: 50px;
}

.indent3{
    margin-left: 10px;
    margin-bottom: -5px;
}



.rightside {
    float: right;
}


/*      LINE SPACING      */


/*line spacing for citations*/
#bibli {
    line-height: 1.5;
    margin-bottom: 15px;
}

/*line spacing for equations */
.spacing {
    line-height: 2.5rem;
}

/*line spacing for list items*/
.textlist {
    margin-bottom: 15px;
}
/* padding at the bottom of the page */
.nine {
    padding-bottom: 80px;
}


/*       CREATING GRID FOR GRAPHS     */

.grid {
    display: flex;
    flex-direction: column;
}

.grid1 {
    width: 50%;
    margin-right: 5px;
    margin-left: 5px;
}

.grid2 {
    display: flex;
    flex-direction: row;
    margin-bottom: 10px;
}

/*design for tables*/


/*design for tables*/

table {
    border: 2px solid black;
    border-collapse: collapse;
    width: 100%;
    margin-top: -10px;
    margin-bottom: 36px;
}

td, th{
    padding: 10px 20px;
    border: 2px solid black;
    text-align: center;
}

.tablecap {
    margin-top: 20px;
}

@media only screen and (min-width: 1440px) {
    /* adjusts for larger than a typical laptop screen */
    .content {
        width: 60%;
    }
    .image{
        width: 403px;
        height: auto;
        margin: 0 auto;
        display: block;
    }
    .image2{
        width: 806px;
        height: auto;
        margin: 0 auto;
        display: block;
    }
    
    .image3{
        width: 605px;
        height: auto;
        margin: 0 auto;
        display: block;
    }
    .grid1 {
        width: 504px;
        margin-right: 5px;
        margin-left: 5px;
    }
    .grid2 {
        display: flex;
        justify-content: center;
    }
}

/* SMALLER */

@media only screen and (min-width: 1232px) and (max-width: 1400px) {
    .navbar-fixed-top-black{
        width: 80%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 72px;
    }
    .image{
        width: 45%;
    } 
    .image2 {
        width: 80%;
    }
    .image3{
        width: 65%;
    }
}

@media only screen and (min-width: 1097px) and (max-width: 1231px) {
    .navbar-fixed-top-black{
        width: 95%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 72px;
    }
    .image{
        width: 50%;
    } 
    .image2 {
        width: 85%;
    }
    .image3{
        width: 70%;
    }
}

@media only screen and (min-width: 990px) and (max-width: 1096px) {
    .navbar-fixed-top-black{
        width: 100%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 72px;
    }
    a{
        font-size: 1rem;
    }
    .content{
        width: 75%;
    }
    .image{
        width: 60%;
    } 
    .image2 {
        width: 90%;
    }
    .image3{
        width: 75%;
    }
}

@media only screen and (min-width: 870px) and (max-width: 989px) {
    .navbar-fixed-top-black{
        width: 100%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 60px;
    }
    a{
        font-size: 1rem;
    }
    h1 {
        font-size: 2.5rem;
    }
    .content{
        width: 80%;
    }
    .image{
        width: 60%;
    } 
    .image2 {
        width: 90%;
    }
    .image3{
        width: 80%;
    }
}

@media only screen and (min-width: 660px) and (max-width: 869px) {
    .navbar-fixed-top-black{
        width: 100%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 40px;
    }
    a{
        font-size: 1rem;
    }
    h1 {
        font-size: 2.25rem;
    }
    .content{
        width: 85%;
    }
    /* width of images */
    .image{
        width: 70%;
    } 
    
    .image2, .image3{
        width: 90%;
    }
    .grid1 {
        width: 50%;
        margin-top: 5px;
        margin-bottom: 5px;
    }
    .grid2 /*changing direction from row to col*/{
        display: flex;
        flex-direction: row;
    }

    /* shortening equation indents*/
    .indent {
        text-indent: 20px;
        font-size: .85rem;
    }
    .indent1 {
        text-indent: 70px;
        margin-bottom: 20px;
    }
    .indent2{
        text-indent: 10px;
    }
    table {
        border: 0px solid black;
    }
    table  { margin-top:  20px; display: inline-block; overflow: auto; }
    th div { margin-top: -20px; position: absolute; }
}



@media only screen and (min-width: 400px) and (max-width: 669px) {
    .navbar-fixed-top-black{
        width: 100%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 10px;
    }
    a {
        font-size: 1rem;
    }
    h1 {
        font-size: 2rem;
    }
    h2 {
        font-size: 1.35rem;
    }
    h3, .sect /*main section headings 1,2,etc*/ {
        font-size: 1rem;
    }
    /*width of page*/
    .content{
        width: 90%;
    }

    .sect1, .sect2 /*section heading directly following main section heading #.x */{
        font-size: 1rem;
    }
    .sect1b, .sect2b /*section heading directly following main section heading #.x.y */{
        font-size: 1rem;
    }
    .graphcap {
        font-size: .8rem;
    }
    .inline_eq{
        font-size: .85rem;
    }

    /* width of images */
    .image{
        width: 80%;
    } 
    
    .image2, .image3{
        width: 100%;
    }
    .grid1 {
        width: 100%;
        margin-top: 5px;
        margin-bottom: 5px;
    }
    .grid2 /*changing direction from row to col*/{
        display: flex;
        flex-direction: column;
    }

    /* shortening equation indents*/
    .indent {
        text-indent: 20px;
        font-size: .85rem;
    }
    .indent1 {
        text-indent: 70px;
        margin-bottom: 20px;
    }
    .indent2{
        text-indent: 10px;
    }
    table {
        border: 0px solid black;
    }
    table  { margin-top:  20px; display: inline-block; overflow: auto; }
    th div { margin-top: -20px; position: absolute; }
}

/*phone size*/

@media only screen and (max-width: 399px) {
    /*nav bar*/
    .navbar-fixed-top-black{
        width: 100%;
    }
    .navbar-fixed-top-black li{
        padding: 0px 5px;
    }
    a {
        font-size: 1rem;
    }

    /* font sizes */
    h1 {
        font-size: 1.75rem;
    }
    h2 {
        font-size: 1.25rem;
    }
    h3, .sect /*main section headings 1,2,etc*/ {
        font-size: 1rem;
    }
    .sect1, .sect2 /*section heading directly following main section heading #.x */{
        font-size: 1rem;
    }
    .sect1b, .sect2b /*section heading directly following main section heading #.x.y */{
        font-size: 1rem;
    }
    .graphcap {
        font-size: .8rem;
    }
    .inline_eq{
        font-size: .85rem;
    }

    /*width of page*/
    .content{
        width: 90%;
    }

    /* width of images */
    .image, .image2, .image3{
        width: 100%;
    }
    .grid1 {
        width: 100%;
        margin-top: 5px;
        margin-bottom: 5px;
    }
    .grid2 /*changing direction from row to col*/{
        display: flex;
        flex-direction: column;
    }

    /* shortening equation indents*/
    .indent {
        text-indent: 0px;
        font-size: .85rem;
    }
    .indent1 {
        text-indent: 25px;
        margin-bottom: 20px;
    }
    .indent2{
        text-indent: 0px;
        font-size: .9rem;
        line-height: 3;
    }
   .shrinkfont{
       font-size: .9rem;
   }

    table {
        border: 0px solid black;
    }
    table  { margin-top:  20px; display: inline-block; overflow: auto; }
    th div { margin-top: -20px; position: absolute; }
}