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3 years ago

Zarah pays the same amount for each text message she sends.

Mathematics

1 answer:

balu736 [363]3 years ago

5 0

Answer:

Step-by-step explanation:

First you divide 4.16 by 52 to get the cost per message which is .08

Then you divide 5.12 by .08 to get the total amount of text messages that month.

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A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the

lord [1]

Answer:

a. -5 ft per sec

b. 59.5 ft² per sec

Step-by-step explanation:

a. Suppose l represents the ladder, x represents the height of the top of ladder from the base of house and y represents the distance of base of ladder from the base of house.

By the Pythagoras theorem,

$l^2 = x^2 + y^2------(1)$

Differentiating with respect to t ( time ),

$2l\frac{dl}{dt} = 2x \frac{dx}{dt}+2y\frac{dy}{dt}$

But, height of ladder, l = 13 ft = constant,

$\implies \frac{dl}{dt}=0$

$\implies 0= 2x \frac{dx}{dt}+2y\frac{dy}{dt}-----(2)$

We have,

y = 5, $\frac{dy}{dt}=12\text{ ft per sec}$ ,

Again by equation (1),

$13^2 = x^2 + 5^2\implies 169 = x^2 + 25\implies 169 - 25 = x^2\implies 144 = x^2\implies x = 12\text{ ft}$

From equation (2),

$0 = 2(12) \frac{dx}{dt} + 2(12)(5)$

$0= 24\frac{dx}{dt}+120$

$-120 =24\frac{dx}{dt}$

$\implies \frac{dx}{dt}=-\frac{120}{24}=-5\text{ ft per sec}$

Hence, the rate of change of the height of the top of the ladder is -5 ft per sec.

b. Now area of the triangle = 1/2 × base × height

$\implies A = \frac{1}{2}\times y\times x$

Differentiating with r. t. t,

$\frac{dA}{dt}=\frac{1}{2}(y\frac{dx}{dt}+x\frac{dy}{dt})$

$= \frac{1}{2}(5(-5) + 12(12))$

$=\frac{1}{2}(-25 + 144)$

$=\frac{119}{2}$

= 59.5 ft² per sec

Hence, area of the triangle is changing with the rate of 59.5 ft per sec.

7 0

4 years ago

Which phrase represents the algebraic expression 3d+7?

Anna [14]

Answer:

3 multiplied by a variable d and add seven to it

Step-by-step explanation:

3 multiplied by a variable d and add seven to it.

6 0

3 years ago

Please help<br><br> 9.4c−1.01*(22b−5.2c)+b

Masteriza [31]

Answer:

14.652c-21.22b

Step-by-step explanation:

multiply parentheses by -1.01

9.4c-22.22b+5.252c+b

collect like terms

14.652c-21.22b

8 0

4 years ago

Read 2 more answers

Help help math please please

wlad13 [49]

$\underline{\underline{\large\bf{Solution:-}}}\\$

The standard form of a line is given by -

$\green{ \underline { \boxed{ \sf{Ax+By=C}}}}$

where

A= integer
x = x-intercept
B= integer
y = y-intercept
C = constant

<h3><u>Given Equation: - </u></h3>

$\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} -1 \\\end{gathered}$

Arranging equation in standard form -

$\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{1}{1} \quad (1 = \frac{1}{1})\\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{1 \times 4}{1 \times 4} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{4}{4} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf y = \frac{-5x-4}{4} \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 4y = -5x-4 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 4y +5x =-4 \\\end{gathered}$

$\begin{gathered}\\\implies\quad \sf 5x +4y=-4 \\\end{gathered}$

Comparing with standard form of line -

A = 5
B = 4

Thus , 5 is our required answer.

8 0

3 years ago

At a zoo 3 pandas eat a total of 181 1/2 pounds of bambu

Ket [755]

What's the question?

7 0

4 years ago

Read 2 more answers