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diamong [38]
2 years ago
8

Bob swam a total of 250 meters on Monday and Tuesday. On Tuesday, the numbers of meters he swam was 30 less than 3 times the amo

unt he swam on Monday. How many meters did Bob swim on Monday?
Mathematics
1 answer:
Sonja [21]2 years ago
7 0

Answer:

Bob swam 70 meters on Monday

Step-by-step explanation:

Let x = Meters swam on Monday

and y = Meters swam on Tuesday

x + y = 250

y = 250 - x

y = 3x - 30

250 - x = 3x - 30

4x = 280

x = 70

y = 180

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PLEASE HELP ME IM STRUGGLING!!!
Kitty [74]

Answer:

The required answer is c=7\sqrt{3}

Therefore the number in green box should be 7.

Step-by-step explanation:

Given:

AB = 7√2

AD = a , BD = b , DC = c , AC = d

∠B = 45°, ∠C = 30°

To Find:

c = ?

Solution:

In Right Angle Triangle ABD Sine identity we have

\sin B = \dfrac{\textrm{side opposite to angle B}}{Hypotenuse}\\

Substituting the values we get

\sin 45 = \dfrac{AD}{AB}= \dfrac{a}{7\sqrt{2}}

\dfrac{1}{\sqrt{2}}= \dfrac{a}{7\sqrt{2}}\\\\\therefore a=7

Now in Triangle ADC Tangent identity we have

\tan C = \dfrac{\textrm{side opposite to angle C}}{\textrm{side adjacent to angle C}}

Substituting the values we get

\tan 30 = \dfrac{AD}{DC}= \dfrac{a}{c}\\\\\dfrac{1}{\sqrt{3}}=\dfrac{7}{c}\\\\\therefore c=7\sqrt{3}

The required answer is c=7\sqrt{3}

8 0
3 years ago
A sphere of radius r is cut by a plane h units above the equator, where
Anika [276]
Consider the top half of a sphere centered at the origin with radius r, which can be described by the equation

z=\sqrt{r^2-x^2-y^2}

and consider a plane

z=h

with 0. Call the region between the two surfaces R. The volume of R is given by the triple integral

\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx

Converting to polar coordinates will help make this computation easier. Set

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

Now, the volume can be computed with the integral

\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta

You should get

\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)
5 0
3 years ago
He earns $37 for 4 hours and 64.75 for 7 hours. what is the constant of proportionality
pogonyaev

Answer:

my answer is 9.25

Step-by-step explanation:

4 0
3 years ago
Which congruence is used in triangulation?
Sedbober [7]
Side angle side (SAS)
7 0
3 years ago
PLEASE ANSWER WILL GIVE 75 POINTS!!!!!
alexdok [17]

Answer:

\frac{4}{33} and \frac{1}{27}

Step-by-step explanation:

We require 2 equations with the repeating numbers placed after the decimal point.

let x = 0.1212...... (1) ← multiply both sides by 10

100x = 12.1212.... (2)

subtract (1) from (2) thus eliminating the repeating numbers

99x = 12 ( divide both sides by 99 )

x = \frac{12}{99} = \frac{4}{33} ← in simplest form

-------------------------------------------------------

let x = 0.037037....... (1) ← multiply both sides by 1000

1000x = 37.037037..... (2)

subtract (1) from (2) to eliminate the repeating numbers

999x = 37 ( divide both sides by 999 )

x = \frac{37}{999} = \frac{1}{27} ← in simplest form

8 0
2 years ago
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